The invention concerns a processing device for a plurality of source digital signals, composed of measurement samples of the signals to be analysed, comprising a correction device for a covariance matrix, representative of the relations between the source signals.
The determination of covariance matrices associated with a set of digital source is signals is used in numerous fields to analyse the properties of the source signals, in particular correlations between these signals. It is notably the case when processing digital signals requiring an assessment of linear models, for example for designing filters, image processing, in weather forecast, etc. . . . . It is also used in automation, notably when designing linear command laws obtained by techniques such as the so-called LQG technique (linear quadratic Gaussian) as well as in the field of finance, as a risk analysis tool.
Conventional covariance determination devices, generally integrated to a digital signal processor (DSP), are most often designed in avoid as much bias as possible on the variances and the covariances associated with a set of digital signals. However, the current techniques do not provide with correct values for the spectrum of the covariance matrix, composed of the set of the proper values of the matrix. The bias on the spectrum of the covariance matrix may notably be high when the measurement samples of the signals to be analysed are low. The smallest proper values of the matrix are underestimated and the largest are overestimated. The conditioning of the matrix, i.e. the ratio of its largest proper value to its smallest proper value is, consequently, erroneous.
Still, when the matrix is used as an input of a digital processing device of the signal, bad conditioning often results in unstable outputs of the processing device thereby disturbing the source signals.
The purpose of the invention is to provide a processing device comprising a covariance matrix correction device enabling to improve the conditioning of the matrix and to define a stable correction as regards small disturbances of the source signals, in order to reduce the difference between an a priori assessment and an a posteriori assessment of variances and of covariances.
According to the invention, this target is met in that the correction device comprises means for decomposition into total proper elements, according to the Kato spectral decomposition method, providing the total proper values of the covariance matrix to be corrected and of the first coefficient vectors, for the combination of the source signals, whereby the correction device comprises correction means using the total proper values and the first coefficient vectors in order to determine the corrected matrix.
According to a development of the invention, the correction device comprises means for determining, by a user, second coefficient vectors for the combination of the source signals.
According to a preferred embodiment, the correction means comprise means for assessing combination variances of the source signals using the first and/or the second coefficient vectors.
According to another characteristic of the invention, the correction device comprises means for searching for the corrected matrix closest to the matrix to be corrected, in relation to the variances supplied by the assessment means and total projectors provided by the means for decomposition into total proper elements.
The searching means apply, preferably, a quasi-Newton type method to the dual of a semi-defined least error square programme